MEASURING FRACTAL DIMENSIONS - SENSITIVITY TO EDGE-PROCESSING FUNCTIONS

The fractal dimension is a useful tool in quantitative histology and c ytology, and its measurement is easily implemented on computerized ima ge analysis systems. However, the optimal conditions for capture of im ages and the effect of image-processing functions on the measurement o f the fractal dimension have not been reported. Edge-processing functi ons were applied to images of Euclidean (square) and fractal (Koch isl and, venal angiogram) objects. The fractal dimension of processed imag es was measured using implementation of the box-counting method, and t he area of thresholded image was also recorded. The method was shown t o be accurate, with errors of <1.5% for objects with known fractal dim ensions, and highly reproducible, with a reliability coefficient of 0. 972 (95% confidence limits of 0.868-0.987). The fractal dimension of t he fractal images showed a marked (> 15%) reduction when a binary nois e reduction function was applied with the minimum neighbors limit set above 3. In contrast, the fractal dimension of the Euclidean square wa s unchanged by this function. The reduction in fractal dimension was d ue to the erosion of complex convolutions at the edge of the fractal o bjects. Edge-processing functions should be avoided when manipulating images of fractal objects.